Estimating Earth's Atmospheric Electrical Energy Potential: A Calculation Guide

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Earths potential?

Homework Statement



the problem reads as folloed
Energy prospectors from a distant planet are inspecting the Earth to decide if its electrical energy resources are worth stealing. Measurements reveal that Earth's electric field extends upward for 800 m and has an average magnitude of 190 V/m. Estimate the electrical energy stored in the atmosphere.

our TA gave us a hint and said
You may treat the atmosphere as a flat slab with an area equal to the surface area of the earth.



The Attempt at a Solution



i tried to derive an equation. i keep getting the wrong answer so please check my math and see if I am doing it wrong or just some calculation error.

i started with
U=1/2 Eo * E^2 Eo is 8.85e^-12
then i went to
U=EV substitued V=4/3pir^3 so got
U=E4/3pi*r^3
this is where i got stuck. i asked my TA and he said i was doing good so far.
i played around with some stuff and got my U (potential) as follows
U=E4pi*r^2*d
but i get the wrong answer. any help would be great ;)
thanks
 
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fball558 said:
our TA gave us a hint and said
You may treat the atmosphere as a flat slab with an area equal to the surface area of the earth.

You're using the wrong volume, it's not a solid sphere.

What is the surface area of the Earth?
What is the volume of a slab that has that area, and the thickness given in the problem statement?